Student sense-making in an intermediate algebra classroom: Investigating student understanding of slope

In this dissertation study, the researcher describes seven sense-snaking opportunities that community college intermediate algebra students experienced to aid in their understanding of slope. A classroom environment was established where students engaged in discourse with their peers while working on classroom tasks focused on a functions approach to mathematical modeling. Research literature shows that students who have not experienced mathematics as a sense-making activity have negative attitudes toward mathematics. In this study, the researcher describes students' changing attitudes toward mathematics and discusses the extent to which these changes are attributed to the supportive classroom environment, classroom discourse, and modeling tasks.; Using qualitative research methods, the researcher analyzes classroom and individual student interview transcripts, student written work, and surveys. Two theoretical frameworks guide this study. The National Council of Teachers of Mathematics Professional Standards for Teaching Mathematics provides a framework emphasizing the important decisions that a teacher makes in teaching. This framework was used to guide the classroom experience. The researcher develops a framework for understanding slope, drawing from the research literature describing covariational reasoning and proportional reasoning, distinguishing between ratio and rate, as well as detailing student understanding of slope. The findings indicate the functions approach to modeling helped students in their sense-making efforts about slope. This approach also helped students understand and make predictions about the modeling situation. The classroom discourse allowed students to share, compare, evaluate, argue, and reflect on their conceptions of slope. Student struggles to make sense of slope were documented. These struggles can be used to inform researchers and practitioners about ways that classroom tasks might be developed to provide improved opportunities for students to make sense of slope.; This study calls for multiple experiences for students to make sense of slope. A robust, multi-faceted understanding of slope takes time. Students' attitudes toward mathematics were positively impacted. Further, longitudinal research is recommended to ascertain the impact that multiple, positive classroom experiences would have on students' ability to understand the concept of slope and on student attitudes toward mathematics.